Calibration of lithographic apparatus by exposing patterns on substrate positioned at different orientations

ABSTRACT

A system and method for calibrating system parameters of a lithography apparatus is disclosed. The system includes a measurement device configured to measure an overlay error between patterns formed on a substrate during different exposures and a processing device configured to determine a model representative of a relationship between the overlay error and a system parameter error based on the measured overlay error. The method includes measuring an overlay error between patterns formed at different exposures with the substrate positioned at different orientations during each of the different exposures. The method further includes determining a model representative of a relationship between the overlay error and a system parameter error based on the measured overlay error and deriving a calibration correction factor from the model.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims benefit under 35 U.S.C. 119(e) to U.S.Provisional Patent Application 61/306,096, filed Feb. 19, 2010, which isincorporated by reference herein in its entirety.

BACKGROUND

1. Field of the Invention

The present invention relates to methods of calibration of alithographic apparatus.

2. Related Art

A lithographic apparatus is a machine that applies a desired patternonto a substrate, usually onto a target portion of the substrate. Alithographic apparatus can be used, for example, in the manufacture ofintegrated circuits (ICs). In that instance, a patterning device, whichis alternatively referred to as a mask or a reticle, may be used togenerate a circuit pattern to be formed on an individual layer of theIC. This pattern can be transferred onto a target portion (e.g.,comprising part of, one, or several dies) on a substrate (e.g., asilicon wafer). Transfer of the pattern is typically via imaging onto alayer of radiation-sensitive material (resist) provided on thesubstrate. In general, a single substrate will contain a network ofadjacent target portions that are successively patterned. Knownlithographic apparatus include so-called steppers, in which each targetportion is irradiated by exposing an entire pattern onto the targetportion at one time, and so-called scanners, in which each targetportion is irradiated by scanning the pattern through a radiation beamin a given direction (the “scanning”-direction) while synchronouslyscanning the substrate parallel or anti-parallel to this direction. Itis also possible to transfer the pattern from the patterning device tothe substrate by imprinting the pattern onto the substrate.

In order to monitor the lithographic process, it is necessary to measureparameters of the patterned substrate, for example the overlay errorbetween successive layers formed in or on it and critical line width ina developed metrology target. There are various techniques for makingmeasurements of the microscopic structures formed in lithographicprocesses, including the use of scanning electron microscopes andvarious specialized tools. A fast and non-invasive form of specializedinspection tool is a scatterometer in which a beam of radiation isdirected onto a target on the surface of the substrate and properties ofthe scattered or reflected beam are measured. By comparing theproperties of the beam before and after it has been reflected orscattered by the substrate, the properties of the substrate can bedetermined. This can be done, for example, by comparing the reflectedbeam with data stored in a library of known measurements associated withknown substrate properties. Two main types of scatterometer are known.Spectroscopic scatterometers direct a broadband radiation beam onto thesubstrate and measure the spectrum (intensity as a function ofwavelength) of the radiation scattered into a particular narrow angularrange. Angularly resolved scatterometers use a monochromatic radiationbeam and measure the intensity of the scattered radiation as a functionof angle.

When a lithography system is first installed it must be calibrated toensure optimal operation. However over time, system performanceparameters will drift. The key system performance parameters that aresubject to drift are the overlay and focus stability of the lithographicapparatus.

A small amount of drift can be tolerated, but too much drift means thatthe system will go out of specification. This problem increases withsmaller chip features. As chip features get smaller, so do thetolerances, or the process window, that manufacturers must work within.The smaller the process window the harder it is to manufacture chipsthat work properly.

Therefore, wafer manufacturers who use lithography apparatus need toperiodically stop production for recalibration of the lithographyapparatus. Calibrating the system more frequently can yield a largerprocess window, but means more scheduled down time.

In order to reduce the frequency at which production must be stopped toperform calibrations, additional calibrations can be performed on thebasis of standard measurements retrieved from a monitor or a referencewafer. The monitor wafer can be exposed using a specialized reticlecontaining special scatterometry marks. From the measurements, it can bedetermined how far the system performance parameters have drifted fromtheir ideal performance levels and wafer level overlay and focuscorrection sets can be calculated. These correction sets can then beconverted into specific corrections for each exposure on subsequentproduction wafers.

This off-tool method using monitor wafers can be performed on a moreregular basis than the full scale calibrations, for example on a dailybasis or every other day, without having to stop production. These moreregular corrections enable compliance with a narrower process window andimprovement in system parameter stability.

Further efficiencies can be realized by using a golden scanner grid,e.g., a map of overlay errors, as the baseline for measuring overlaystability, instead of using random monitoring wafers, meaning thatoverlay grid matching and long term stability can be achieved in oneautomated step.

However, even given the benefits of making these types of corrections,there are associated problems. The reference wafers are re-used and thusare subject to aging. An etched grid can be reused for only twenty tothirty reworks before the monitor wafers need to be replaced, which canhave a negative impact on the work in progress. The initial grid qualitygoverns the accuracy of the correction process and deteriorates with theage of the monitor wafers.

SUMMARY

Therefore, what is needed is an effective system and method ofcorrecting for errors in system parameters of lithographic apparatusthat can increase the accuracy of calibration of the lithographicapparatus.

In an embodiment of the present invention, there is provided a method ofdetecting errors in system parameters of a lithographic apparatus thatincludes performing a number of exposures to form markers on asubstrate, with the substrate positioned at a different orientation foreach exposure and then measuring the overlay between correspondingmarkers formed from the different exposures.

In a further embodiment of the present invention, there is provided amethod of calibrating a lithographic apparatus that includes detectingerrors in system parameters of a lithographic apparatus by performing anumber of exposures to form markers on a substrate with the substratebeing positioned at a different orientation for each exposure and thenmeasuring the overlay between corresponding markers formed from thedifferent exposures thereby obtaining system parameter errors from themeasured overlay. The method also provides for deriving calibrationcorrection factors from the obtained system parameter errors.

In a still further embodiment of the present invention, there isprovided a lithographic apparatus that includes an illuminator arrangedto perform a number of exposures to form markers on a substrate with thesubstrate being positioned at a different orientation for each exposureand a measurement device arranged to measure the overlay betweencorresponding markers formed from the different exposures.

In a still further embodiment of the present invention, there isprovided a lithographic apparatus that includes an illuminator arrangedto perform a number of exposures to form markers on a substrate with thesubstrate being positioned at a different orientation for each exposure,and a measuring device arranged to measure the overlay betweencorresponding markers formed from different exposures with a computerarranged to obtain system parameter errors from the measured overlay andto derive calibration correction factors from the obtained systemparameter errors.

Further embodiments, features, and advantages of the present invention,as well as the structure and operation of various embodiments of theinvention, are described in detail below with reference to theaccompanying drawings. It is noted that the invention is not limited tothe specific embodiments described herein. Such embodiments arepresented herein for illustrative purposes only. Additional embodimentswill be apparent to persons skilled in the relevant art(s) based on theteachings contained herein.

BRIEF DESCRIPTION OF THE DRAWINGS/FIGURES

Embodiments of the invention will now be described, by way of exampleonly, with reference to the accompanying schematic drawings in whichcorresponding reference symbols indicate corresponding parts. Further,the accompanying drawings, which are incorporated herein and form partof the specification, illustrate the present invention, and, togetherwith the description, further serve to explain the principles of theinvention and to enable a person skilled in the relevant art(s) to makeand use the invention.

FIG. 1 depicts a lithographic apparatus, according to an embodiment ofthe present invention.

FIG. 2 depicts a lithographic cell or cluster, according to anembodiment of the present invention.

FIG. 3 depicts a first scatterometer, according to an embodiment of thepresent invention.

FIG. 4 depicts a second scatterometer, according to an embodiment of thepresent invention.

FIG. 5 is a schematic diagram showing components of a lithographicapparatus having separate measurement and exposure stages, according toan embodiment of the present invention.

FIG. 6 illustrates schematically the stages in the measurement andexposure processes in the apparatus of FIG. 5, according to anembodiment of the present invention.

FIG. 7 depicts a first example of an arrangement for moving wafer stageson a substrate, according to an embodiment of the present invention.

FIG. 8 depicts a second example of an arrangement for moving waferstages on a substrate, according to an embodiment of the presentinvention.

The features and advantages of the present invention will become moreapparent from the detailed description set forth below when taken inconjunction with the drawings, in which like reference charactersidentify corresponding elements throughout. In the drawings, likereference numbers generally indicate identical, functionally similar,and/or structurally similar elements.

DETAILED DESCRIPTION

This specification discloses one or more embodiments that incorporatethe features of this invention. The disclosed embodiment(s) merelyexemplify the invention. The scope of the invention is not limited tothe disclosed embodiment(s). The invention is defined by the claimsappended hereto.

The embodiment(s) described, and references in the specification to “oneembodiment,” “an embodiment,” “an example embodiment,” etc., indicatethat the embodiment(s) described may include a particular feature,structure, or characteristic, but every embodiment may not necessarilyinclude the particular feature, structure, or characteristic. Moreover,such phrases are not necessarily referring to the same embodiment.Further, when a particular feature, structure, or characteristic isdescribed in connection with an embodiment, it is understood that it iswithin the knowledge of one skilled in the art to affect such feature,structure, or characteristic in connection with other embodimentswhether or not explicitly described.

Embodiments of the invention may be implemented in hardware, firmware,software, or any combination thereof. Embodiments of the invention mayalso be implemented as instructions stored on a machine-readable medium,which may be read and executed by one or more processors. Amachine-readable medium may include any mechanism for storing ortransmitting information in a form readable by a machine (e.g., acomputing device). For example, a machine-readable medium may includeread only memory (ROM); random access memory (RAM); magnetic diskstorage media; optical storage media; flash memory devices; electrical,optical, acoustical or other forms of propagated signals (e.g., carrierwaves, infrared signals, digital signals, etc.), and others. Further,firmware, software, routines, instructions may be described herein asperforming certain actions. However, it should be appreciated that suchdescriptions are merely for convenience and that such actions in factresult from computing devices, processors, controllers, or other devicesexecuting the firmware, software, routines, instructions, etc.

Before describing such embodiments in more detail, however, it isinstructive to present an example environment in which embodiments ofthe present invention may be implemented.

FIG. 1 schematically depicts a lithographic apparatus, according to anembodiment of the present invention. The apparatus includes anillumination system (illuminator) IL configured to condition a radiationbeam B (e.g., UV radiation or DUV radiation); a support structure (e.g.,a mask table) MT constructed to support a patterning device (e.g., amask) MA and connected to a first positioner PM configured to accuratelyposition the patterning device in accordance with certain parameters; asubstrate table (e.g., a wafer table) WT constructed to hold a substrate(e.g., a resist-coated wafer) W and connected to a second positioner PWconfigured to accurately position the substrate in accordance withcertain parameters; and a projection system (e.g., a refractiveprojection lens system) PL configured to project a pattern imparted tothe radiation beam B by patterning device MA onto a target portion C(e.g., comprising one or more dies) of the substrate W.

The illumination system may include various types of optical components,such as refractive, reflective, magnetic, electromagnetic,electrostatic, or other types of optical components, or any combinationthereof, for directing, shaping, or controlling radiation.

The support structure supports, i.e., bears the weight of, thepatterning device. It holds the patterning device in a manner thatdepends on the orientation of the patterning device, the design of thelithographic apparatus, and other conditions, such as for examplewhether or not the patterning device is held in a vacuum environment.The support structure can use mechanical, vacuum, electrostatic, orother clamping techniques to hold the patterning device. The supportstructure may be a frame or a table, for example, which may be fixed ormovable as required. The support structure may ensure that thepatterning device is at a desired position, for example with respect tothe projection system. Any use of the terms “reticle” or “mask” hereinmay be considered synonymous with the more general term “patterningdevice.”

The term “patterning device” used herein should be broadly interpretedas referring to any device that can be used to impart a radiation beamwith a pattern in its cross-section such as to create a pattern in atarget portion of the substrate. It should be noted that the patternimparted to the radiation beam may not exactly correspond to the desiredpattern in the target portion of the substrate, for example if thepattern includes phase-shifting features or so called assist features.Generally, the pattern imparted to the radiation beam will correspond toa particular functional layer in a device being created in the targetportion, such as an integrated circuit.

The patterning device may be transmissive or reflective. Examples ofpatterning devices include masks, programmable mirror arrays, andprogrammable LCD panels. Masks are well known in lithography, andinclude mask types such as binary, alternating phase-shift, andattenuated phase-shift, as well as various hybrid mask types. An exampleof a programmable mirror array employs a matrix arrangement of smallmirrors, each of which can be individually tilted so as to reflect anincoming radiation beam in different directions. The tilted mirrorsimpart a pattern in a radiation beam, which is reflected by the mirrormatrix.

The term “projection system” used herein should be broadly interpretedas encompassing various types of projection system, includingrefractive, reflective, catadioptric, magnetic, electromagnetic andelectrostatic optical systems, or any combination thereof, asappropriate for the exposure radiation being used, or for other factorssuch as the use of an immersion liquid or the use of a vacuum. Any useof the term “projection lens” herein may be considered as synonymouswith the more general term “projection system.”

In this embodiment, for example, the apparatus is of a transmissive type(e.g., employing a transmissive mask). Alternatively, the apparatus maybe of a reflective type (e.g., employing a programmable mirror array ofa type as referred to above, or employing a reflective mask).

The lithographic apparatus may be of a type having two, e.g., dualstage, or more substrate tables and, for example, two or more masktables. In such “multiple stage” machines the additional tables may beused in parallel, or preparatory steps may be carried out on one or moretables while one or more other tables are being used for exposure.

The lithographic apparatus may also be of a type wherein at least aportion of the substrate may be covered by a liquid having a relativelyhigh refractive index, e.g., water, so as to fill a space between theprojection system and the substrate. An immersion liquid may also beapplied to other spaces in the lithographic apparatus, for example,between the mask and the projection system. Immersion techniques arewell known in the art for increasing the numerical aperture ofprojection systems. The term “immersion” as used herein does not meanthat a structure, such as a substrate, must be submerged in liquid, butrather only means that liquid is located between the projection systemand the substrate during exposure.

Referring to FIG. 1, the illuminator IL receives a radiation beam from aradiation source SO. The source and the lithographic apparatus may beseparate entities, for example when the source is an excimer laser. Insuch cases, the source is not considered to form part of thelithographic apparatus and the radiation beam is passed from the sourceSO to the illuminator IL with the aid of a beam delivery system BDcomprising, for example, suitable directing mirrors and/or a beamexpander. In other cases the source may be an integral part of thelithographic apparatus, for example when the source is a mercury lamp.The source SO and the illuminator IL, together with the beam deliverysystem BD if required, may be referred to as a radiation system.

The illuminator IL may comprise an adjuster AD for adjusting the angularintensity distribution of the radiation beam. Generally, at least theouter and/or inner radial extent, which are commonly referred to asσ-outer and σ-inner, respectively, of the intensity distribution in apupil plane of the illuminator can be adjusted. In addition, theilluminator IL may comprise various other components, such as anintegrator IN and a condenser CO. The illuminator may be used tocondition the radiation beam, to have a desired uniformity and intensitydistribution in its cross-section.

The radiation beam B is incident on the patterning device (e.g., maskMA), which is held on the support structure (e.g., mask table MT), andis patterned by the patterning device. Having traversed the mask MA, theradiation beam B passes through the projection system PL, which focusesthe beam onto a target portion C of the substrate W. With the aid of thesecond positioner PW and position sensor IF (e.g., an interferometricdevice, linear encoder, 2-D encoder or capacitive sensor), the substratetable WT can be moved accurately, e.g., so as to position differenttarget portions C in the path of the radiation beam B. Similarly, thefirst positioner PM and another position sensor (which is not explicitlydepicted in FIG. 1) can be used to accurately position the mask MA withrespect to the path of the radiation beam B, e.g., after mechanicalretrieval from a mask library, or during a scan. In general, movement ofthe mask table MT may be realized with the aid of a long-stroke module(coarse positioning) and a short-stroke module (fine positioning), whichform part of the first positioner PM. Similarly, movement of thesubstrate table WT may be realized using a long-stroke module and ashort-stroke module, which form part of the second positioner PW. In thecase of a stepper (as opposed to a scanner) the mask table MT may beconnected to a short-stroke actuator only, or may be fixed. Mask MA andsubstrate W may be aligned using mask alignment marks M1, M2, andsubstrate alignment marks P1, P2. Although the substrate alignment marksas illustrated occupy dedicated target portions, they may be located inspaces between target portions, which are known as scribe-lane alignmentmarks. Similarly, in situations in which more than one die is providedon the mask MA, the mask alignment marks may be located between thedies.

The depicted apparatus could be used in at least one of the followingmodes:

1. In step mode, the mask table MT and the substrate table WT are keptessentially stationary, while an entire pattern imparted to theradiation beam is projected onto a target portion C at one time (i.e., asingle static exposure). The substrate table WT is then shifted in the Xand/or Y direction so that a different target portion C can be exposed.In step mode, the maximum size of the exposure field limits the size ofthe target portion C imaged in a single static exposure.

2. In scan mode, the mask table MT and the substrate table WT arescanned synchronously while a pattern imparted to the radiation beam isprojected onto a target portion C (i.e., a single dynamic exposure). Thevelocity and direction of the substrate table WT relative to the masktable MT may be determined by the (de-)magnification and image reversalcharacteristics of the projection system PL. In scan mode, the maximumsize of the exposure field limits the width (in the non-scanningdirection) of the target portion in a single dynamic exposure, whereasthe length of the scanning motion determines the height (in the scanningdirection) of the target portion.

3. In another mode, the mask table MT is kept essentially stationaryholding a programmable patterning device, and the substrate table WT ismoved or scanned while a pattern imparted to the radiation beam isprojected onto a target portion C. In this mode, generally a pulsedradiation source is employed and the programmable patterning device isupdated as required after each movement of the substrate table WT or inbetween successive radiation pulses during a scan. This mode ofoperation can be readily applied to maskless lithography that utilizesprogrammable patterning device, such as a programmable mirror array of atype as referred to above.

Combinations and/or variations on the above described modes of use orentirely different modes of use may also be employed.

As shown in FIG. 2, according to an embodiment of the present invention,the lithographic apparatus LA forms part of a lithographic cell LC, alsosometimes referred to a lithocell or cluster, which also includesapparatus to perform pre- and post-exposure processes on a substrate.Conventionally these include spin coaters SC to deposit resist layers,developers DE to develop exposed resist, chill plates CH and bake platesBK. A substrate handler, or robot, RO picks up substrates frominput/output ports I/O1, I/O2, moves them between the different processapparatus and delivers then to the loading bay LB of the lithographicapparatus. These devices, which are often collectively referred to asthe track, are under the control of a track control unit TCU that isitself controlled by the supervisory control system SCS, which alsocontrols the lithographic apparatus via lithography control unit LACU.Thus, the different apparatus can be operated to maximize throughput andprocessing efficiency.

In order that the substrates that are exposed by the lithographicapparatus are exposed correctly and consistently, it is desirable toinspect exposed substrates to measure properties such as overlay errorsbetween subsequent layers, line thicknesses, critical dimensions (CD),etc. If errors are detected, adjustments, for example, may be made toexposures of subsequent substrates, especially if the inspection can bedone soon and fast enough that other substrates of the same batch arestill to be exposed. Also, already exposed substrates may be strippedand reworked to improve yield or to possibly be discarded, therebyavoiding performing exposures on substrates that are known to be faulty.In a case where only some target portions of a substrate are faulty,further exposures can be performed only on those target portions thatare deemed to be non-faulty.

An inspection apparatus is used to determine the properties of thesubstrates, and in particular, how the properties of differentsubstrates or different layers of the same substrate vary from layer tolayer. The inspection apparatus may be integrated into the lithographicapparatus LA or the lithocell LC or may be a stand-alone device. Toenable most rapid measurements, it is desirable that the inspectionapparatus measure properties in the exposed resist layer immediatelyafter the exposure. However, the latent image in the resist has a verylow contrast, as in there is only a very small difference in refractiveindex between the parts of the resist that have been exposed toradiation and those that have not, and not all inspection apparatus havesufficient sensitivity to make useful measurements of the latent image.Therefore measurements may be taken after the post-exposure bake step(PEB) that is customarily the first step carried out on exposedsubstrates and increases the contrast between exposed and unexposedparts of the resist. At this stage, the image in the resist may bereferred to as semi-latent. It is also possible to make measurements ofthe developed resist image at which point either the exposed orunexposed parts of the resist have been removed or after a patterntransfer step such as etching. The latter possibility limits thepossibilities for rework of faulty substrates but may still provideuseful information.

FIG. 3, according to an embodiment of the present invention, depicts ascatterometer SM1 that may be used in the present invention. Itcomprises a broadband (white light) radiation projector 2 that projectsradiation onto a substrate W. The reflected radiation is passed to aspectrometer detector 4, which measures a spectrum 10 (intensity as afunction of wavelength) of the specular reflected radiation. From thisdata, the structure or profile giving rise to the detected spectrum maybe reconstructed by processing unit PU, e.g., by Rigorous Coupled WaveAnalysis and non-linear regression or by comparison with a library ofsimulated spectra as shown at the bottom of FIG. 3. In general, for thereconstruction the general form of the structure is known and someparameters are assumed from knowledge of the process by which thestructure was made, leaving only a few parameters of the structure to bedetermined from the scatterometry data. Such a scatterometer may beconfigured as a normal-incidence scatterometer or an oblique-incidencescatterometer.

Another scatterometer SM2 that may be used with the present invention isshown in FIG. 4, according to an embodiment of the present invention. Inthis device, the radiation emitted by radiation source 2 is collimatedusing lens system 12 and transmitted through interference filter 13 andpolarizer 17, reflected by partially reflected surface 16 and is focusedonto substrate W via a microscope objective lens 15, which has a highnumerical aperture (NA), for example, preferably at least about 0.9, andmore preferably at least about 0.95. Immersion scatterometers may evenhave lenses with numerical apertures over 1. The reflected radiationthen transmits through partially reflecting surface 16 into a detector18 in order to have the scatter spectrum detected. The detector may belocated in the back-projected pupil plane 11, which is at the focallength of the lens system 15, however the pupil plane may instead bere-imaged with auxiliary optics (not shown) onto the detector. The pupilplane is the plane in which the radial position of radiation defines theangle of incidence and the angular position defines azimuth angle of theradiation. In one example, the detector is a two-dimensional detector sothat a two-dimensional angular scatter spectrum of a substrate target 30can be measured. The detector 18 may be, for example, an array of CCD orCMOS sensors, and may use an integration time of, for example, 40milliseconds per frame.

A reference beam is often used for example to measure the intensity ofthe incident radiation. To do this, when the radiation beam is incidenton the beam splitter 16 part of it is transmitted through the beamsplitter as a reference beam towards a reference mirror 14. Thereference beam is then projected onto a different part of the samedetector 18 or alternatively on to a different detector (not shown).

A set of interference filters 13 is available to select a wavelength ofinterest in the range of, for example, 405-790 nm, or even lower, suchas 200-300 nm. The interference filter may be tunable rather thancomprising a set of different filters. A grating could be used insteadof interference filters.

The detector 18 can measure the intensity of scattered light at a singlewavelength, or in a narrow wavelength range, the intensity separately atmultiple wavelengths or integrated over a wavelength range. Furthermore,the detector can separately measure the intensity of transverse magneticand transverse electric polarized light and/or the phase differencebetween the transverse magnetic and transverse electric polarized light.

Using a broadband light source (i.e., one with a wide range of lightfrequencies or wavelengths, and therefore a wide range of colors ispossible, which gives a large Etendue, allowing the mixing of multiplewavelengths. The plurality of wavelengths in the broadband preferablyeach has a bandwidth of Δλ and a spacing of at least 2 Δλ (i.e., twicethe bandwidth). A plurality of “sources” of radiation can be differentportions of an extended radiation source that have been split usingfiber bundles. In this way, angle resolved scatter spectra can bemeasured at multiple wavelengths in parallel. A 3-D spectrum, forexample, such as wavelength and two different angles, can be measured,which contains more information than a 2-D spectrum. This allows moreinformation to be measured that increases metrology process robustness.This is described in more detail in European Patent No. 1,628,164A,which is incorporated by reference herein in its entirety.

The target 30 on substrate W may be a 1-D grating, which is printed suchthat after development, the bars are formed of solid resist lines. Thetarget 30 can be a 2-D grating, which is printed such that afterdevelopment, the grating is formed of solid resist pillars or vias inthe resist. The bars, pillars, or vias may alternatively be etched intothe substrate. This pattern is sensitive to chromatic aberrations in thelithographic projection apparatus, particularly the projection systemPL, and illumination symmetry and the presence of such aberrations willmanifest themselves in a variation in the printed grating. Accordingly,the scatterometry data of the printed gratings is used to reconstructthe gratings. The parameters of the 1-D grating, such as line widths andshapes, or parameters of the 2-D grating, such as pillar or via widthsor lengths or shapes, can be input to the reconstruction process,performed by processing unit PU, from knowledge of the printing stepand/or other scatterometry processes.

FIG. 5, according to an embodiment of the present invention, showsschematically the arrangement of one embodiment of the apparatus of FIG.1, in which the apparatus is of the type having dual substrate supportsand separate metrology and exposure stations.

A base frame FB supports and surrounds the apparatus on the ground.Within the apparatus, and serving as an accurate positional reference, ametrology frame FM is supported on air bearings 402, which isolate itfrom vibrations in the environment. Mounted on this frame are theprojection system PS, which naturally forms the core of the exposurestation EXP, and also instruments 404, 406, 408, which are thefunctional elements of the metrology station MET. Above these stations,the mask table MT and mask MA are mounted above the projection systemPS. The first positioner PM comprises long-throw (coarse) actuators 410and short-throw (fine) actuators 412, 414. These operate by activefeedback control to obtain the desired position of mask MA with respectto the projection system PS, and hence with respect to metrology frameFM. This measurement is indicated schematically at 416. The wholepositioning mechanism for the mask MA is supported on the base frame atB via active air bearings 418 etc. A balance mass 420 is provided tomimic at least coarse movements of the mask table MT and positioning, toreduce vibrations being transmitted into the frame and other components.A low frequency servo control keeps balance mass 420 in a desiredaverage position. Wafer table WT shown beneath the projection systemsimilarly has coarse actuators 422 and fine actuators 424, 426 forpositioning substrate W accurately with respect to the exit lens of theprojection system PS. Additionally, according to the dual-stagearrangement of this example, a duplicate wafer table WT′ and positioningmechanism PW′ are provided. As illustrated, these duplicate elements aresupporting a second substrate W′ at the metrology station MET. Wafertables WT, WT′ and their respective positioners PW and PW′ are carriedon and connected to a shared balance mass 428. Again, air bearings, orother suitable bearings such as magnetic, electrostatic, and so forth,are shown schematically, for example at 430. Measurements of wafer tableposition used for the coarse and fine control of the positions of thewafers W and W′ are made relative to elements 406 at the metrologystation and PS at the exposure station, both of these ultimatelyreferring back to metrology frame FM.

FIG. 6, according to an embodiment of the present invention, illustratesthe steps in this twin-stage apparatus of FIG. 5 to expose dies on asubstrate W. On the left hand side within a dotted box are stepsperformed at metrology station MET, while the right hand side showssteps performed at the exposure station EXP. A substrate W has alreadybeen loaded into the exposure station. A new substrate W′ is loaded tothe apparatus by a mechanism not shown at step 500. These two substratesare processed in parallel in order to increase the throughput of themetrology process as a whole. Referring initially to the newly-loadedsubstrate W′, this may be a previously unprocessed substrate, preparedwith a new photo resist for first time exposure in the apparatus. Ingeneral, however, the lithography process described will be merely onestep in a serious of exposure and processing steps, so that substrate W′has been through this apparatus and/or other lithography apparatusseveral times already, and may have subsequent processes to undergo aswell. At 502, alignment measurements using the substrate marks P1 etc.and image sensors etc. are used to measure and record alignment of thesubstrate relative to substrate table WT. In practice, several marksacross the substrate W′ will be measured, to establish the “wafer grid,”that maps very accurately the distribution of marks across thesubstrate, including any distortion relative to a nominal regular grid.At step 504, a map of wafer height against X-Y position is measuredalso, for use in accurate focusing of the exposed pattern.

When substrate W′ was loaded, recipe data 506 are received, defining theexposures to be performed, and also properties of the wafer and thepatterns previously made and to be made upon it. To these recipe dataare added the measurements made at 502, 504, so that a complete set ofrecipe and metrology data 508 can be passed to the exposure stage. At510, wafers W′ and W are swapped, so that the measured substrate W′becomes the substrate W entering the exposure apparatus. This swappingis performed by exchanging the supports WT and WT′ within the apparatus,so that the substrates W, W′ remain accurately clamped and positioned onthose supports, to preserve relative alignment between the substratetables and substrates themselves. Accordingly, once the tables have beenswapped, determining the relative position between projection system PSand substrate table WT (formerly WT′) is all that is necessary to makeuse of the measurement information 502, 504 for the substrate W(formerly W′) in control of the exposure steps. At step 512, reticlealignment is performed using mask alignment marks. In steps 514, 516,518, scanning motions and radiation pulses are applied at successive dielocations across substrate W, in order to complete the exposure of anumber of patterns. Thanks to the alignment and level map data, thesepatterns are accurately aligned with respect to desired locations, and,in particular, with respect to features previously laid down on the samesubstrate. The exposed substrate, now labeled W″ is unloaded from theapparatus at step 520, to undergo etching or other processes, inaccordance with the exposed pattern.

By employing the separate substrate tables, the performance of theapparatus in terms of substrate throughput through the exposure stagesis maintained, while permitting a relatively time-consuming set ofmeasurements to be performed to characterize the wafer and patternspreviously deposited upon it.

As mentioned above, the wafer table WT shown in FIG. 1 and wafer tablesWT, WT′ shown in FIG. 5 have coarse actuators 422 and fine actuators424, 426 for positioning substrate W accurately with respect to the exitlens of the projection system PS.

There are different known mechanisms for moving the wafer table and masktables and for measuring their positions. One such system isschematically illustrated in FIG. 7 and uses a planar motor to drive thetwo wafer tables WT and WT′. The balance mass 428 in this embodimentcomprises a magnet plate, and the undersides of the wafer tables WT andWT′ comprise force actuators for movement of the tables in the x, y andz directions (the z direction being out of the plane of the page). Inthe system of the type illustrated in FIG. 7, the position of the tablesWT and WT′ is measured via encoders that are located on the underside ofa metrology frame (shown as FM in FIG. 5), and an image sensor isprovided on the relevant wafer chuck to monitor the position via theencoders of the tables. The encoders cooperate to output a location ofthe wafer tables in (x,y) coordinates.

An alternative embodiment is shown in FIG. 8, according to an embodimentof the present invention. Here the positions of the wafer tables WT, WT′on the balance mass 428 are controlled via actuators 800, 800′ formoving the tables in an x direction, e.g., left and right as shown inthe figure, and actuators 802, 802′ for moving the tables in a ydirection, e.g., up and down as shown in the figure. The positions ofthe tables WT, WT′ are measured by interferometers that project beamsonto mirrored side wall surfaces of the wafer tables. Typically an “x”interferometer provides the location of one wafer table in an x axis,and a “y” interferometer provides the location of one wafer table in ay-axis. Each of the “x” and “y” interferometers may comprisetransmitters at both sides of the balance mass 428, arranged to directinterferometer beams towards opposing sides of the wafer tables.

The present disclosure relates to embodiments in which system parametersare checked through self-assessment of a production substrate, that is,without the need for a reference or a monitor wafer. In particular,errors derived from mirror or substrate deformation, as well as encodererrors, can be corrected.

The calibration method of the disclosure can be carried out on a regularbasis, one or more times between calibration of machine constants; orone or more times between measurement of offsets with monitor wafers; orone or more times between measurement of lot offsets. The choice of whenand how often the calibration method of this disclosure is applieddepends on the characteristics of the particular process involved, andthe desired trade off between calibration accuracy and throughput.However, as the use of a monitor wafer is not required, the applicationof the method of the present disclosure can be carried out without asevere deleterious effect on throughput, as will become apparent fromthe description to follow.

Aspects of this disclosure can be embodied in control software thatresides in a lithographic apparatus, or alternatively, the aspects canbe embodied in a stand-alone calibration device that can performmeasurements on a wafer that has been exposed.

In a multiple stage lithographic apparatus, the exposure steps can becarried out at an exposure station, and the measurement steps can becarried out at a metrology station.

The required data storage and calculations can be carried out by acomputer that usually is integrated with the lithographic apparatus butcould be provided as a separate device. The computer is also arranged togenerate control signals that can be used to modify the systemparameters of the lithography system on the basis of calculatedcorrection factors.

Aspects of this disclosure are also applicable to any mode of use of alithographic apparatus, including step mode, scan mode, other modes thatuse a programmable patterning device and a pulsed radiation source; ormodes that comprise various combinations of these techniques.

The self-assessment of a product substrate according to this disclosurecan comprise exposing a substrate in at least two differentorientations, and measuring the overlay between corresponding markersformed from different exposures.

It should be appreciated that the exposure of a substrate in at leasttwo different orientations means that the substrate is intentionallypositioned at a first orientation and then rotated to a secondorientation.

In one embodiment, the substrate can be exposed with a specializedreticle containing special scatterometry marks. Normally, thesescatterometry marks consist of two parts (boxes or gratings). One ormore first marker portions of these scatterometry markers can be exposedwith one exposure, and one or more second marker portions can be exposedwith a different exposure, where the substrate has a differentorientation as compared to the case of the orientation during the firstexposure. The two portions are designed to overlap to form a compositemarker. This composite marker can then be measured, and any overlayerrors between the first and second marker portions then give arepresentation of the system parameter errors.

The method of this embodiment may be carried out on a substrate that isalready pre-etched with reference markers, and can if desired be carriedout by an off-tool measurement device.

In an alternative embodiment, two similar sets of markers can be exposedwith each different exposure. They are designed to be in alignment, andany overlay errors between the two markers then give a representation ofthe system parameter errors.

The system parameter errors that can be represented include for examplescan/step direction offset, positioning and deformation errors, as wellas intrafield errors.

The exposure positions are chosen such that it is possible to measureoverlay between two layers that are exposed in different orientations,for example, overlay between a layer exposed in a normal waferorientation and layer exposed when wafer is rotated on 180 degrees.

For example, if a marker is horizontally oriented and consist ofregularly spaced gratings, an alignment sensor measuring this marker candetermine the X position of the marker. If then we rotate this marker by90 degrees, an alignment sensor can give Y information. If we expose onehorizontal marker in 0 degree and another in 180 and readout bothmarkers, we get two (or difference between these two) horizontalpositions. Both markers will be seen during alignment as markers of onetype (horizontal). On the other hand, if two markers are exposed in anarbitrary rotation, we would end up in two differently orientedstructures on the wafer that will not be seen as markers on the sametype.

It should be noted that for the two-part composite markers of the typementioned above, there is a requirement that the different orientationsstill yield a properly formed composite marker. At least two differentorientations are required, although more can be used if required, inorder to provide more accurate readings of the errors being measured.The angular difference between the orientations is arbitrary althoughfor good results an angular difference of 90 degrees would be useful.For example, measurements could be carried out for one or more of 0 vs.90; 90 vs. 180; 180 vs. 270; or 270 vs. 360 degrees orientations.

It will be appreciated that the definition of the reference orientationof 0 degrees is also arbitrary.

Similarly to wafer grid errors, intrafield (scanning reticle stage)errors could be determined.

The overlay information is used to determine a polynomial model fordifferent causes. Polynomial representation of a model is used to reducenoise to calibration and to make a calibration generic for arbitraryexposure positions.

This can be represented by the notation below, in which the terms“upper,” “lower,” “left,” and “right” refer to positions of neighboringexposure areas on the wafer. The designation of these terms isessentially arbitrary. In the figures, these directions correspond tothe orientation of the pages.

The following applies firstly to types of mechanisms for moving thewafer table and mask tables and for measuring their positions that use xand y interferometers, such as that shown in FIG. 8 for example.

The step dependency of the mirror deformation can be represented by:dx _(—)0−dx _(—)180˜Sum(a _(—) n*(sign(step_direction_(—)0)*y_(—)0^n−sign(step_direction_(—)180)*y _(—)180^n)).

In this and subsequent notation, the x and y subscripts denote the angleof orientation of the relevant exposure. That is, the difference in themeasured x-position between a first exposure taken at an orientation of0 degrees and a second exposure taken at an orientation of 180 degreesis approximately equal to

$\sum\limits_{n = 0}^{N}{{a_{n}\left( {{{{sgn}\left( {step\_ direction}_{0} \right)}y_{0}^{n}} - {{{sgn}\left( {step\_ direction}_{180} \right)}y_{180}^{n}}} \right)}.}$Here, sgn is the signum function, where sgn(a)=+1 if a>0; 0 if a=0 and−1 if a<0. The step direction is the direction with respect to a waferat the zero degree position.

Similarly, dy_(—)0−dy_(—)180˜Sum(b_n*(sign(step_direction_(—)0)*x_(—)0^n−sign(step_direction_(—)180)*x_(—)180^n)).That is, the difference in the measured y-position between a firstexposure taken at an orientation of 0 degrees and a second exposuretaken at an orientation of 180 degrees is approximately equal to

$\sum\limits_{n = 0}^{N}{{b_{n}\left( {{{{sgn}\left( {step\_ direction}_{0} \right)}x_{0}^{n}} - {{{sgn}\left( {step\_ direction}_{180} \right)}x_{180}^{n}}} \right)}.}$[Also, another positioning error can be described as dy˜P(x)]

The scan dependency of mirror deformation can be represented by:dx _(—)0−dx _(—)180˜Sum(c _(—) n*(sign(scan_direction_(—)0)*y_(—)0^n−sign(scan_direction_(—)180)*y _(—)180^n)).

That is, the difference in the measured x-position between a firstexposure taken at an orientation of 0 degrees and a second exposuretaken at an orientation of 180 degrees is approximately equal to

$\sum\limits_{n = 0}^{N}{{c_{n}\left( {{{{sgn}\left( {scan\_ direction}_{0} \right)}y_{0}^{n}} - {{{sgn}\left( {scan\_ direction}_{180} \right)}y_{180}^{n}}} \right)}.}$

Similarly, dy_(—)0−dy_(—)180˜Sum(d_n*(sign(scan_direction_(—)0)*x_(—)0^n−sign(scan_direction_(—)180)*x_(—)180^n)).That is, the difference in the measured y-position between a firstexposure taken at an orientation of 0 degrees and a second exposuretaken at an orientation of 180 degrees is approximately equal to

$\sum\limits_{n = 0}^{N}{{d_{n}\left( {{{{sgn}\left( {scan\_ direction}_{0} \right)}x_{0}^{n}} - {{{sgn}\left( {scan\_ direction}_{180} \right)}x_{180}^{n}}} \right)}.}$

The two-dimensional effect on the wafer of deformation in x and ydirections can be represented by two-dimensional polynomials

The step dependency of wafer deformation can be represented by:dx _(—)0−dx _(—)180=Sum(Sum(e _(—) n _(—) m*(sign(step_direction_(—)0)*x_(—)0^n*y _(—)0^N−m−sign(step_direction_(—)180)*x _(—)180^n*y_(—)180^N−m))).

That is, the difference in the measured x-position between a firstexposure taken at an orientation of 0 degrees and a second exposuretaken at an orientation of 180 degrees is approximately equal to

${\sum\limits_{n = 0}^{N}{\sum\limits_{m = n}^{N}{e_{n,m}\left( {{{{sgn}\left( {step\_ direction}_{0} \right)}x_{0}^{n}y_{0}^{N - m}} - {{sgn}\left( {step\_ direction}_{180} \right)x_{180}^{n}y_{180}^{N - m}}} \right)}}}..$

Similarly,dy _(—)0−dy _(—)180=Sum(Sum(f _(—) n _(—) m*(sign(step_direction_(—)0)*x_(—)0^n*y _(—) 0^N−m−sign(step_direction_(—)180)*x _(—)180^n*y_(—)180^N−m))).

That is, the difference in the measured y-position between a firstexposure taken at an orientation of 0 degrees and a second exposuretaken at an orientation of 180 degrees is approximately equal to

${\sum\limits_{n = 0}^{N}{\sum\limits_{m = n}^{N}{f_{n,m}\left( {{{{sgn}\left( {step\_ direction}_{0} \right)}x_{0}^{n}y_{0}^{N - m}} - {{sgn}\left( {step\_ direction}_{180} \right)x_{180}^{n}y_{180}^{N - m}}} \right)}}}..$

The scan dependency of wafer deformation can be represented by:dx _(—)0−dx _(—)180=Sum(Sum(g _(—) n _(—) m*(sign(scan_direction_(—)0)*x_(—)0^n*y _(—)180^m−sign(scan_direction_(—)180)*x _(—)180^n*y_(—)180^m))).

That is, the difference in the measured x-position between a firstexposure taken at an orientation of 0 degrees and a second exposuretaken at an orientation of 180 degrees is approximately equal to

${\sum\limits_{n = 0}^{N}{\sum\limits_{m = n}^{N}{g_{n,m}\left( {{{{sgn}\left( {scan\_ direction}_{0} \right)}x_{0}^{n}y_{0}^{N - m}} - {{{sgn}\left( {scan\_ direction}_{180} \right)}x_{180}^{n}y_{180}^{N - m}}} \right)}}}..$

Similarly,dy _(—)0−dy _(—)180=Sum(Sum(h _(—) n _(—) m*(sign(scan_direction_(—)0)*x_(—)0^n*y _(—)0^m−sign(scan_direction_(—)180)*x _(—)180^n*y_(—)180^m))).

That is, the difference in the measured y-position between a firstexposure taken at an orientation of 0 degrees and a second exposuretaken at an orientation of 180 degrees is approximately equal to:

${\sum\limits_{n = 0}^{N}{\sum\limits_{m = n}^{N}{h_{n,m}\left( {{{{sgn}\left( {scan\_ direction}_{0} \right)}x_{0}^{n}y_{0}^{N - m}} - {{{sgn}\left( {scan\_ direction}_{180} \right)}x_{180}^{n}y_{180}^{N - m}}} \right)}}}..$

It is also possible to apply similar aspects to the types of mechanismsfor moving the wafer table and mask tables and for measuring theirpositions that use encoders that output (x,y) coordinates, such as thatshown in FIG. 7 for example.

In that case, the step direction can be represented by:(dx _(—)0,dy _(—)0)−(dx _(—)180,dy _(—)180)=Encodermodel((sign(step_direction_(—)0)−sign(step_direction_(—)180))*h_step)

where h_step is a vector that characterizes encoder displacement causedby a stepping move. Here, the difference in measured (x,y) coordinatesbetween a first exposure taken at an orientation of 0 degrees and asecond exposure taken at an orientation of 180 degrees is described bythe displacement of encoders as application the Encoder model to(sgn(step_direction_(—)0)−sgn(step_direction_(—)180))*h_step). The“Encoder model” referred to here is a positioning model, representing atransformation from measured encoder values (h) to a position (q) of ameasured object in a Cartesian coordinate system (for example having sixdegrees of freedom, namely the offset in X, Y and Z as well as rotationand tilt of wafer stage (Rz, Rx, Ry)). The model can be described ash=A*q+C*r(q). For some applications we can assume that h=A*q, ignoringhigh order or cross-terms. In the present case, q=B*h, where B=A⁻¹. Itis a simplified linear model that can be read as a transformation from h(encoder) to q (only horizontal offset in (x,y) coordinates). The errorbetween an upper exposed field and a neighboring lower exposed field(x,y) positions is derived from the encoder model applied to thedifference of errors on encoders induced by stepping direction(h_(step)) where h_(step) is the encoder error caused by stepping inpositive direction (along the X axis). The scan direction can berepresented by: (dx_(—)0,dy_(—)0)−(dx_(—)180,dy_(—)180)=Encodermodel((sign(scan_direction_(—)0)−sign(scan_direction_(—)180))*h_scan).That is, the difference in measured (x,y) coordinates between a firstexposure taken at an orientation of 0 degrees and a second exposuretaken at an orientation of 180 degrees is equal to the Encoder modelapplied to((sign(scan_direction_(—)0)−sign(scan_direction_(—)180))*h_scan).

Wafer deformation can be represented by:dx _(—)0−dx _(—)180=Sum(Sum(r _(—) n _(—) m*(x _(—)0^n*y0^N−m−x_(—)180^n*y _(—)180^N−m))).

That is, the difference in the measured x-position between a firstexposure taken at an orientation of 0 degrees and a second exposuretaken at an orientation of 180 degrees is equal to

$\sum\limits_{n = 0}^{N}{\sum\limits_{m = n}^{N}{{r_{n,m}\left( {{x_{0}^{n}y_{0}^{N - m}} - {x_{180}^{n}y_{180}^{N - m}}} \right)}.}}$

Similarly,dy_(—)0−dy _(—)180=Sum(Sum(s _(—) n _(—) m*(x _(—)0^n*y _(—)0^N−m−x_(—)180^n*y _(—)180^N−m))).

That is, the difference in the measured y-position between a firstexposure taken at an orientation of 0 degrees and a second exposuretaken at an orientation of 180 degrees is equal to

$\sum\limits_{n = 0}^{N}{\sum\limits_{m = n}^{N}{{s_{n,m}\left( {{x_{0}^{n}y_{0}^{N - m}} - {x_{180}^{n}y_{180}^{N - m}}} \right)}.}}$

Aspects of this disclosure can also be used to correct for mirror errorsfor interferometer systems. For the types of mechanisms for moving thewafer table and mask tables and for measuring their positions that use xand y interferometers, such as that shown in FIG. 8 for example, themirror errors can be represented by:dx_(—)0−dx_(—)180˜Sum(t_n*(y_(—)0−y_(—)180^n)). That is, the differencein the measured x-position between a first exposure taken at anorientation of 0 degrees and a second exposure taken at an orientationof 180 degrees is approximately equal to

$\sum\limits_{n = 0}^{N}{{t_{n}\left( {y_{0}^{n} - y_{180}^{n}} \right)}.}$

Similarly, dy_(—)0−dy_(—)180˜Sum(u_n*(x_(—)0^n−x_(—)180^n)). That is,the difference in the measured y-position between a first exposure takenat an orientation of 0 degrees and a second exposure taken at anorientation of 180 degrees is approximately equal to

$\sum\limits_{n = 0}^{N}{{u_{n}\left( {x_{0}^{n} - x_{180}^{n}} \right)}.}$

For types of mechanisms for moving the wafer table and mask tables andfor measuring their positions that use encoders that output (x,y)coordinates, such as that shown in FIG. 7 for example, the encodererrors can be represented by:(dx _(—)0,dy _(—)0)−(dx _(—)180,dy _(—)180)=Encoder_model(Sum(Sum(v _(—)i _(—) n _(—) m*(x _(—)0^n*y _(—)0^N−m−x _(—)180^n*y _(—) 180^N−m)))).

That is, the difference in measured (x,y) coordinates between a firstexposure taken at an orientation of 0 degrees and a second exposuretaken at an orientation of 180 degrees is equal to q₀−q₁₈₀=Bh where h isa vector with each element having the following representation

${h_{i} = {\sum\limits_{n = 0}^{N}{\sum\limits_{m = n}^{N}{v_{i,n,m}x^{n}y^{N - m}}}}},{q_{0} = \left( {{dx}_{0},{dy}_{0}} \right)},{q_{180} = \left( {{dx}_{180},{dy}_{180}} \right)}$and B represents encoder model.

Once the difference between errors (in all the above examples) ondifferent wafer positions has been determined, it is possible to use thedetermined dy_(—)0−dy_(—)180 to create a linear problem for determiningpolynomial coefficients s that minimize the relative error. Thesecoefficients can be used for correction during further exposure. Thelinear problem may take the form of:∥A*s−b∥−>min

where A depends on the specific polynomial appropriate for the type oferror being considered (for example, in the immediately preceding caseA=x_(—)0^n*y_(—)0^N−m−x_(—)180^n*y_(—)180^N−m), b is the measureddifference {dy_(—)0−dy_(—)180} and s is a solution (polynomialcoefficients). Clearly the above examples for calculation ofdx_(—)0−dx_(—)180 and (dx_(—)0,dy_(—)0)−(dx_(—)180,dy_(—)180) can betreated in an equivalent way.

Although specific reference may be made in this text to the use oflithographic apparatus in the manufacture of ICs, it should beunderstood that the lithographic apparatus described herein may haveother applications, such as the manufacture of integrated opticalsystems, guidance and detection patterns for magnetic domain memories,flat-panel displays, liquid-crystal displays (LCDs), thin film magneticheads, etc. The skilled artisan will appreciate that, in the context ofsuch alternative applications, any use of the terms “wafer” or “die”herein may be considered as synonymous with the more general terms“substrate” or “target portion”, respectively. The substrate referred toherein may be processed, before or after exposure, in for example atrack (a tool that typically applies a layer of resist to a substrateand develops the exposed resist), a metrology tool and/or an inspectiontool. Where applicable, the disclosure herein may be applied to such andother substrate processing tools. Further, the substrate may beprocessed more than once, for example in order to create a multi-layerIC, so that the term substrate used herein may also refer to a substratethat already contains multiple processed layers.

Although specific reference may have been made above to the use ofembodiments of the invention in the context of optical lithography, itwill be appreciated that the invention may be used in otherapplications, for example imprint lithography, and where the contextallows, is not limited to optical lithography. In imprint lithography atopography in a patterning device defines the pattern created on asubstrate. The topography of the patterning device may be pressed into alayer of resist supplied to the substrate whereupon the resist is curedby applying electromagnetic radiation, heat, pressure or a combinationthereof. The patterning device is moved out of the resist leaving apattern in it after the resist is cured.

The terms “radiation” and “beam” used herein encompass all types ofelectromagnetic radiation, including ultraviolet (UV) radiation (e.g.,having a wavelength of or about 365, 355, 248, 193, 157 or 126 nm) andextreme ultra-violet (EUV) radiation (e.g., having a wavelength in therange of 5-20 nm), as well as particle beams, such as ion beams orelectron beams.

The term “lens,” where the context allows, may refer to any one orcombination of various types of optical components, includingrefractive, reflective, magnetic, electromagnetic, and electrostaticoptical components.

While specific embodiments of the invention have been described above,it will be appreciated that the invention may be practiced otherwisethan as described. For example, the invention may take the form of acomputer program containing one or more sequences of machine-readableinstructions describing a method as disclosed above, or a data storagemedium (e.g., semiconductor memory, magnetic or optical disk) havingsuch a computer program stored therein.

It is to be appreciated that the Detailed Description section, and notthe Summary and Abstract sections, is intended to be used to interpretthe claims. The Summary and Abstract sections may set forth one or morebut not all exemplary embodiments of the present invention ascontemplated by the inventor(s), and thus, are not intended to limit thepresent invention and the appended claims in any way.

The present invention has been described above with the aid offunctional building storing blocks illustrating the implementation ofspecified functions and relationships thereof. The boundaries of thesefunctional building storing blocks have been arbitrarily defined hereinfor the convenience of the description. Alternate boundaries can bedefined so long as the specified functions and relationships thereof areappropriately performed.

The foregoing description of the specific embodiments will so fullyreveal the general nature of the invention that others can, by applyingknowledge within the skill of the art, readily modify and/or adapt forvarious applications such specific embodiments, without undueexperimentation, without departing from the general concept of thepresent invention. Therefore, such adaptations and modifications areintended to be within the meaning and range of equivalents of thedisclosed embodiments, based on the teaching and guidance presentedherein. It is to be understood that the phraseology or terminologyherein is for the purpose of description and not of limitation, suchthat the terminology or phraseology of the present specification is tobe interpreted by the skilled artisan in light of the teachings andguidance.

The breadth and scope of the present invention should not be limited byany of the above-described exemplary embodiments, but should be definedonly in accordance with the following claims and their equivalents.

What is claimed is:
 1. A method comprising: performing a plurality ofexposures to form a plurality of patterns on a substrate, the substratebeing positioned at a different orientation during each exposure of theplurality of exposures to form a corresponding pattern of the pluralityof patterns; measuring an overlay error between a first pattern and asecond pattern of the plurality of patterns, the first pattern beingexposed at a first substrate orientation and the second pattern beingexposed at a second substrate orientation, the first and secondsubstrate orientations being different from each other; and determining,based on the measured overlay error, a model representative of arelationship between the overlay error and a system parameter error,wherein the model comprises a polynomial function.
 2. The method ofclaim 1, wherein: the measuring of the overlay error comprises measuringa composite pattern formed from overlapping of the first and secondpatterns.
 3. The method of claim 1, wherein the substrate is aproduction wafer.
 4. A method comprising: performing a plurality ofexposures to form a plurality of patterns on a substrate, the substratebeing positioned at a different orientation during each exposure of theplurality of exposures to form a corresponding pattern of the pluralityof patterns; measuring an overlay error between a first pattern and asecond pattern of the plurality of patterns, the first pattern beingexposed at a first substrate orientation and the second pattern beingexposed at a second substrate orientation, the first and secondsubstrate orientations being different from each other; determining,based on the measured overlay error, a model representative of arelationship between the overlay error and a system parameter error,wherein the model comprises a polynomial function; and deriving acalibration correction factor from the model.
 5. The method of claim 4,wherein the system parameter error comprises a scanning error.
 6. Alithographic apparatus comprising: an illuminator configured to performa plurality of exposures to form a plurality of patterns on a substrate,the substrate being positioned at a different orientation during eachexposure of the plurality of exposures to form a corresponding patternof the plurality of patterns; a measurement device configured to measurean overlay error between a first pattern and a second pattern of theplurality of patterns, the first pattern being exposed at a firstsubstrate orientation and the second pattern being exposed at a secondsubstrate orientation, the first and second substrate orientations beingdifferent from each other; and a processing device configured todetermine, based on the measured overlay error, a model representativeof a relationship between the overlay error and a system parametererror, wherein the model comprises a polynomial function.
 7. Alithographic apparatus comprising: an illuminator configured to performa plurality of exposures to form a plurality of patterns on a substrate,the substrate being positioned at a different orientation during eachexposure of the plurality of exposures to form a corresponding patternof the plurality of patterns; a measuring device configured to measurean overlay error between a first pattern and a second pattern of theplurality of patterns, the first pattern being exposed at a firstsubstrate orientation and the second pattern being exposed at a secondsubstrate orientation, the first and second substrate orientations beingdifferent from each other; and a processing device configured to:determine, based on the measured overlay error, a model representativeof a relationship between the overlay error and a system parametererror, wherein the model comprises a polynomial function; and derive acalibration correction factor from the model.
 8. A non-transitorycomputer-readable medium having computer program logic recorded thereon,execution of which, by a computing device, causes the computing deviceto perform operations comprising: performing a plurality of exposures toform a plurality of patterns on a substrate, the substrate beingpositioned at a different orientation during each exposure of theplurality of exposures to form a corresponding pattern of the pluralityof patterns; measuring an overlay error between a first pattern and asecond pattern of the plurality of patterns, the first pattern beingexposed at a first substrate orientation and the second pattern beingexposed at a second substrate orientation, the first and secondsubstrate orientations being different from each other; and determining,based on the measured overlay error, a model representative of arelationship between the overlay error and a system parameter error,wherein the model comprises a polynomial function.
 9. A non-transitorycomputer-readable medium having computer program logic recorded thereon,execution of which, by a computing device, causes the computing deviceto perform operations comprising: performing a plurality of exposures toform a plurality of patterns on a substrate, the substrate beingpositioned at a different orientation during each exposure of theplurality of exposures to form a corresponding pattern of the pluralityof patterns; measuring an overlay error between a first pattern and asecond pattern of the plurality of patterns, the first pattern beingexposed at a first substrate orientation and the second pattern beingexposed at a second substrate orientation, the first and secondsubstrate orientations being different from each other; determining,based on the measured overlay error, a model representative of arelationship between the overlay error and a system parameter error,wherein the model comprises a polynomial function; and deriving acalibration correction factor from the model.